QUESTION 01

Solve the following equations:

(A)   \(x^2 + 9 = 0\)

(B)   \(x^2 + 2x + 10 = 0\)

QUESTION 02

Express each of the following in the form of \(x + yi\)

(A)   \(3 + 5i) + (7 - 2i)\)

(B)   \(5 - 2i) - (6 + i)\)

(C)   \((5 - 2i)^2\)

(D)   \(\dfrac {8 + 5i}{4 - 3i}\)

QUESTION 03

Find the linear factors of:

(A)   \(z^2 + 4z + 20\)

(B)   \(z^2 - 3z + 6 \frac 14\)

QUESTION 04

Express each of the following in polar form and exponential form:

(A)   \(z = 4 + 3i\)

(B)   \(z = -1 - i\)

QUESTION 05

Let \(z_1 = 4 \text{ cis } \dfrac {\pi}{3}\) and \(z_2 = 2 \text{ cis } \dfrac {5 \pi}{6}\). Determine:

(A)   \(z_1 z_2\)

(B)   \(\dfrac {z_1}{z_2}\)

QUESTION 06

Express each of the following in \(x + yi\) form:

(A)   \((1 + \sqrt{3} i)^6\)

(B)   \((1 - i)^{-7}\)

QUESTION 07

Solve the equation below:

(A)   \(z^3 = 8\)

(B)   \(z^4 = 1 + i \sqrt{3}\)

QUESTION 08

QUESTION 09

QUESTION 10